Dear sirs!

How much money has the client?

Can we help the banker?

This exercise is part of exercises about the subject: "Number theory" and it could be a diophantine equation.

A dispersed bank cashier mistook 1 dollar coins and 1 cent coins when he paid out the cheque of Mr. Brown, while he gave him 1 dollar coins instead of 1 cent coins and 1 cent coins instead of 1 dollar coins. After Mr. Brown had - at home - put generously 5 cents in the savings tin of his son, he discovered that he had exactly twice as much money left over, as had stood on the cheque. On which sum was the cheque drawn?

I've already got the following thoughts:

c= amount of 1 Cent coins

k= amount of 1 Dollar coins

2(100k+c) = k+100c-5

98c = 199k+5

c = 2.03061224k + 0.05263158

Now I tried the numbers from 1 to 500 for c, but k was never an integer number. But because there are only whole coins, and not ones like 0.05678, k and c have to be integer numbers.

Could you tell me what I have to correct?

Or is it just an impossible question?

Thank you in advance!

Sincerly

enoimreh

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